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To solve this problem, we need to determine the function $ A(t) $, which represents the sum of Tamika's assets from the value of her property and inventory. The problem gives the following functions:

- $ R(t) = 500,000 (1.013^t) $: This models the value of her store property $ t $ years after purchase.
- $ I(t) = 100,000 + 40,000t $: This models the value of her store inventory $ t $ years after purchase.

The function $ A(t) $, representing the sum of her assets, is simply the sum of $ R(t) $ and $ I(t) $:

\[
A(t) = R(t) + I(t)
\]

Substituting the given expressions for $ R(t) $ and $ I(t) $:

\[
A(t) = 500,000 (1.013^t) + (100,000 + 40,000t)
\]

This is the function that represents the total value of Tamika's assets over time.

Would you like more details or have any questions?

### 5 Related Questions:
1. How does the growth of property value affect Tamika's total assets over time?
2. Can the asset function $ A(t) $ be graphed, and what are the key features of the graph?
3. What is the rate of growth of Tamika's property value $ R(t) $ compared to the linear growth of her inventory $ I(t) $?
4. At what time $ t $ do Tamika's assets reach a certain value, say \$1,000,000?
5. How would the asset function change if Tamika's inventory increased at a different rate?

### Tip:
When dealing with exponential functions like $ R(t) $, pay attention to the growth rate as it can lead to significant increases over time compared to linear growth.

Tamika owns a retail store with a focus on skincare for African American women. The function R(t) models the value of her store property t years after she purchased it. The function I(t) models the value of her store inventory for the same time period. Which function, A(t), represents the sum of Tamika’s assets, R(t) + I(t)?

Learn how to calculate the total assets of Tamika's store using functions that model exponential and linear growth. This problem provides detailed insights into function addition and models real-world scenarios involving property value and inventory growth. Suitable for students in Grades 10-12.

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